In sci.stat.edu Herman Rubin <[EMAIL PROTECTED]> wrote:
>>Each one of these probability setups 1-3 gives rise to a somewhat
>>different small-sample inferential test. In particular,
>>the schemes (1),(2),(3) give rise to distributions conditioned
>>on 3, 2, and 1 fixed parameters respectively.
> But these parameters are unknown. Testing with nuisance
> parameters is very definitely not easy, and exact tests
> are hard to come by. Even in other types of problems,
I was not here referring to the unknown "nuisance" parameter
(namely the unknown binomial probability). In schemes
(1), (2), (3) the 3, 2, and 1 fixed conditioning parameters
are, respectively: (a) two row marginals and one column
marginal (b) two independent row marginals (c) the
total sum of four cells. In the conditioning arguments
which yield the signficance tests I alluded to above,
those 3, 2, or 1 parameters are *known*.
> As long as the conditional probabilities are the same,
which conditional probabilities are you referring to?
> and one uses one of the scenarios you mentioned, the
> distribution of the Fisher exact test given the marginals
> is as stated. Thus the probability that the test at a
> given level rejects is precisely the stated level in all
> of these cases, assuming that randomized testing is used.
> If one uses a decision approach, none of this is correct,
> even if the Fisher model happens to be true.
I was only addressing the matter of the logical relationship
between the probability model used in the significance test to
the implied underlying sample space of 2x2 tables from which
the observed table was drawn. It seems to me that the
choice of experimental design has some bearing on the choice
of such "universe" and I was wondering why the Fisher Universe
of permutations with 4 fixed marginals is chosen as the
basis for inferential tests for experimental setups in which
quite plainly only *two* marginals can be regarded as fixed
(e.g. case-control studies, & so on). Is there a simple
answer to this question? (I guess there really is not...)
> --
> This address is for information only. I do not claim that these views
> are those of the Statistics Department or of Purdue University.
> Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
> [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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